Continuum quantum systems as limits of discrete quantum systems. III. Operators
Date
2001
Authors
Barker, L.
Editor(s)
Advisor
Supervisor
Co-Advisor
Co-Supervisor
Instructor
Source Title
Journal of Mathematical Physics
Print ISSN
0022-2488
Electronic ISSN
1089-7658
Publisher
A I P Publishing LLC
Volume
42
Issue
10
Pages
4653 - 4668
Language
English
Type
Journal Title
Journal ISSN
Volume Title
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Abstract
Convergence of a "discrete" operator to a "continuum" operator is defined. As examples, the circular rotor, the one-dimensional box, the harmonic oscillator, and the fractional Fourier transform are realized as limits of finite-dimensional quantum systems. Limits, thus defined, preserve algebraic structure. The results prepare for a sequel in which some affine canonical transforms will be "discretized." © 2001 American Institute of Physics.